I suggest that playing in person would be a better introduction to D&D than any computer game. The publisher, wizards of the coast, organizes D&D game days at local game stores around the country. They are free and very newby friendly. A key ingredient of D&D for many, myself included, is the time spent around a table with friends. Online interactions don't fully capture this experience.

Computer games aren't the way to go. If you've played any computer RPG in the last 20 years, you've gotten an introduction and you're ready to take the leap.

Buy the latest Players Handbook, read it for a while, then put together a short adventure for 2-3 friends. Don't worry, it's not hard, and there is no wrong way to do it.

I like Baldurs Gate and Neverwinter Nights. Not exactly new games, but still one of the best PC RPGs. Fallout is also great, but doesn't use the DnD system.